Method and apparatus for delivering a biphasic defibrillation pulse with variable energy

ABSTRACT

An apparatus and method for determining an optimal transchest external defibrillation waveform that provides for variable energy in the first or second phase of a biphasic waveform that, when applied through a plurality of electrodes positioned on a patient&#39;s torso, will produce a desired response in the patient&#39;s cardiac cell membranes. The method includes the steps of providing a quantitative model of a defibrillator circuit for producing external defibrillation waveforms, the quantitative model of a patient includes a chest component, a heart component, a cell membrane component and a quantitative description of the desired cardiac membrane response function. Finally, a quantitative description of a transchest external defibrillation waveform that will produce the desired cardiac membrane response function is computed. The computation is made as a function of the desired cardiac membrane response function, the patient model and the defibrillator circuit model.

RELATED APPLICATIONS

[0001] This application is a continuation application of copendingnon-provisional application Ser. No. 09/678,820, filed Oct. 4, 2000,entitled METHOD AND APPARATUS FOR DELIVERING A BIPHASIC DEFIBRILLATIONPULSE WITH VARIABLE ENERGY, which is a continuation-in-part ofapplication Ser. No. 09/383,561, filed Aug. 26, 1999, entitled METHODAND APPARATUS FOR DETERMINING THE SECOND PHASE OF EXTERNAL DEFIBRILLATORDEVICES, which is a continuation-in-part application of issued U.S. Pat.No. 5,968,080, which is based on provisional patent application Ser. No.60/021,161, filed Jul. 1, 1996 entitled DYNAMIC SECOND PHASE (02) WITHSELF-CORRECTING CHARGE BURPING FOR EXTERNAL DEFIBRILLATOR DEVICES. Thecontents of each of the above-identified applications are herebyincorporated by reference.

FIELD OF THE INVENTION

[0002] This invention relates generally to an electrotherapy method andapparatus for delivering an electrical pulse to a patient's heart. Inparticular, this invention relates to a method and apparatus fortailoring a second phase of biphasic waveform delivered by an externaldefibrillator, to random patients, by performing intelligentcalculations and analysis to the results of a first phase segment of abiphasic defibrillation waveform and other parameters pertaining theretobased on theory and practice as disclosed herein.

BACKGROUND OF THE INVENTION

[0003] Devices for defibrillating a heart have been known for sometimenow. Implantable defibrillators are well accepted by the medicalcommunity as effective tools to combat fibrillation for an identifiedsegment of the population. A substantial amount of research infibrillation and the therapy of defibrillation has been done. Much ofthe most recent research has concentrated on understanding the effectsthat a defibrillation shock pulse has on fibrillation to terminate sucha condition.

[0004] A monophasic waveform is defined to be a single phase,capacitive-discharge, time-truncated, waveform with exponential decay. Abiphasic waveform is defined to comprise two monophasic waveforms,separated by tine and of opposite polarity. The first phase isdesignated Ø₁ and the second phase is designated Ø₂. The delivery of Ø₁is completed before the delivery of Ø₂ is begun.

[0005] After extensive testing, it has been determined that biphasicwaveforms are more efficacious than monophasic waveforms. There is awide debate regarding the reasons for the increased efficacy of biphasicwaveforms over that of monophasic waveforms. One hypothesis holds thatØ₁ defibrillates the heart and Ø₂ performs a stabilizing action thatkeeps the heart from refibrillating.

[0006] Biphasic defibrillation waveforms are now the standard of care inclinical use for defibrillation with implantablecardioverter-defibrillators (ICDs), due to the superior performancedemonstrated over that of comparable monophasic waveforms. To betterunderstand these significantly different outcomes, ICD research hasdeveloped cardiac cell response models to defibrillation. Waveformdesign criteria have been derived from these first principles and havebeen applied to monophasic and biphasic waveforms to optimize theirparameters. These principles-based design criteria have producedsignificant improvements over the current art of waveforms.

[0007] In a two-paper set, Blair developed a model for the optimaldesign of a monophasic waveform when used for electrical stimulation.(1) Blair, H. A., “On the Intensity-time relations for stimulation byelectric currents.” I. J. Gen. Physiol. 1932; 15: 709-729. (2) Blair, H.A., “On the Intensity-time Relations for stimulation by electriccurrents.” II. J. Gen. Physiol. 1932; 15: 731-755. Blair proposed anddemonstrated that the optimal duration of a monophasic waveform is equalto the point in time at which the cell response to the stimulus ismaximal. Duplicating :. Blair's model, Walcott extended Blair's analysisto defibrillation, where they obtained supporting experimental results.Walcott, et al., “Choosing the optimal monophasic and biphasic waveformsfor ventricular defibrillation.” J. Cardiovasc Electrophysiol. 1995; 6:737-750.

[0008] Independently, Kroll developed a biphasic model for the optimaldesign of Ø₂ for a biphasic defibrillation waveform. Kroll, M. W., “Aminimal model of the single capacitor biphasic defibrillation waveform.”PACE 1994; 17:1782-1792. Kroll proposed that the 02 stabilizing actionremoved the charge deposited by Ø₁ from those cells not stimulated by0 1. This has come to be known as “charge burping”. Kroll supported hishypothesis with retrospective analysis of studies by Dixon, et al.,Tang, et al., and Freese, et al. regarding single capacitor, biphasicwaveform studies. Dixon, et al., “Improved defibrillation thresholdswith large contoured epicardial electrodes and biphasic waveforms.”Circulation 1987; 76:1176-1184; Tang, et al. “Ventricular defibrillationusing biphasic waveforms: The Importance of Phasic duration.” J. Am.Coll. Cardiol. 1989; 13:207-214; and Feeser, S. A., et al.“Strength-duration and probability of success curves for defibrillationwith biphasic waveforms.” Circulation 1990; 82: 2128-2141. Again, theWalcott group retrospectively evaluated their extension of Blair's modelto 0 2 using the Tang and Feeser data sets. Their finding furthersupported Kroll's hypothesis regarding biphasic defibrillationwaveforms. For further discussions on the development of these models,reference may be made to PCT publications WO 95/32020 and WO 95/09673and to U.S. Pat. No. 5,431,686.

[0009] The charge burping hypothesis can be used to develop equationsthat describe the time course of a cell's membrane potential during abiphasic shock pulse. At the end of Ø₁, those cells that were notstimulated by Ø₁ have a residual charge due to the action of Ø₁ on thecell. The charge burping model hypothesizes that an optimal pulseduration for Ø₂ is that duration that removes as much of the Ø₁ residualcharge from the cell as possible. Ideally, these unstimulated cells areset back to “relative ground.” The charge burping model proposed byKroll is based on the circuit model shown in FIG. 2b, which is adaptedfrom the general model of a defibrillator illustrated in FIG. 2a.

[0010] The charge burping model also accounts for removing the residualcell membrane potential at the end of a Ø₁ pulse that is independent ofa Ø₂. That is, 4)2 is delivered by a set of capacitors separate from theset of capacitors used to deliver Ø₁. This charge burping model isconstructed by adding a second set of capacitors, as illustrated in FIG.3. In this figure, C₁ represents the Ø₁ capacitor set, C₂ represents theØ₂ capacitor set R_(H) represents the resistance of the heart, and thepair C_(M) and R_(M) represent membrane series capacitance andresistance of a single cell. The node V_(S) represents the voltagebetween the electrodes, while V_(M) denotes the voltage across the cellmembrane.

[0011] External defibrillators send electrical pulses to the patient'sheart through electrodes applied to the patient's torso. Externaldefibrillators are useful in any situation where there may be anunanticipated need to provide electrotherapy to a patient on shortnotice. The advantage of external defibrillators is that they may beused on a patient as needed, then subsequently moved to be used withanother patient.

[0012] However, this important advantage has two fundamentallimitations. First, external defibrillators do not have direct contactwith the patient's heart. External defibrillators have traditionallydelivered their electrotherapeutic pulses to the patient's heart fromthe surface of the patient's chest. This is known as the transthoracicdefibrillation problem. Second, external defibrillators must be able tobe used on patients having a variety of physiological differences.External defibrillators have traditionally operated according to pulseamplitude and duration parameters that can be effective in all patients.This is known as the patient variability problem.

[0013] The prior art described above effectively models implantabledefibrillators, however it does not fully address the transthoracicdefibrillation problem nor the patient variability problem. In fact,these two limitations to external defibrillators are not fullyappreciated by those in the art. For example, prior art disclosures ofthe use of truncated exponential monophasic or biphasic shock pulses inimplantable or external defibrillators have provided little guidance forthe design of an external defibrillator that will successfullydefibrillate across a large, heterogeneous population of patients. Inparticular, an implantable defibrillator and an external defibrillatorcan deliver a shock pulse of similar form, and yet the actualimplementation of the waveform delivery system is radically different.

[0014] In the past five years, new research in ICD therapy has developedand demonstrated defibrillation models that provide waveform designrules from first principles. These defibrillation models and theirassociated design rules for the development of defibrillation waveformsand their characteristics were first developed by Kroll and Imich formonophasic waveforms using effective and rheobase current concepts. (1)Kroll, M. W., “A minimal model of the monophasic defibrillation pulse.”PACE 1993; 15: 769. (2) Irnich, W., “Optimal truncation ofdefibrillation pulses.” PACE 1995; 18: 673. Subsequently, Kroll,Walcott, Cleland and others developed the passive cardiac cell membraneresponse model for monophasic and biphasic waveforms, herein called thecell response model. (1) Kroll, M. W., “A minimal model of the singlecapacitor biphasic defibrillation waveform.” PACE 1994; 17: 1782. (2)Walcott, G. P., Walker, R. G., Cates. A. W., Krassowska, W., Smith, W.M, Ideker R E. “Choosing the optimal monophasic and biphasic waveformsfor ventricular defibrillation.” J Cardiovasc Electrophysiol 1995;6:737; and Cleland B G. “A conceptual basis for defibrillationwaveforms.” PACE 1996; 19:1186).

[0015] A significant increase in the understanding of waveform designhas occurred and substantial improvements have been made by using thesenewly developed design principles. Block et al. has recently written acomprehensive survey of the new principles-based theories and theirimpact on optimizing internal defibrillation through improved waveforms.Block M, Breithardt G., “Optimizing defibrillation through improvedwaveforms.” PACE 1995; 18:526.

[0016] There have not been significant developments in externaldefibrillation waveforms beyond the two basic monophasic waveforms: thedamped sine or the truncated exponential. To date, their design fortransthoracic defibrillation has been based almost entirely onempirically derived data. It seems that the design of monophasic andbiphasic waveforms for external defibrillation has not yet beengenerally influenced by the important developments in ICD research.

[0017] Recently there has been reported research on the development andvalidation of a biphasic truncated exponential waveform in which it wascompared clinically to a damped sine waveform. For additionalbackground, reference may be made to U.S. Pat. Nos. 5,593,427, 5,601,612and 5,607,454. See also: Gliner B. E., Lyster T. E., Dillon S. M., BardyG. H., “Transthoracic defibrillation of swine with monophasic andbiphasic waveforms.” Circulation 1995; 92:1634-1643; Bardy G. H., GlinerB. E., Kudenchuk P. J., Poole J. E., Dolack G. L., Jones G. K., AndersonJ., Troutman C., Johnson G.; “Truncated biphasic pulses fortransthoracic defibrillation.” Circulation 1995; 91:1768-1774; and BardyG. H. et al, “For the Transthoracic Investigators. Multicentercomparison of truncated biphasic shocks and standard damped sine wavemonophasic shocks for transthoracic ventricular defibrillation.”Circulation 1996; 94:2507-2514. Although the research determined ausable biphasic waveform, there was no new theoretical understandingdetermined for external waveform design. It appears that externalwaveform research may develop a “rules-of-thumb by trial and error”design approach much like that established in the early stages oftheoretical ICD research. The noted limitations of the transthoracicbiphasic waveform may be due in part to a lack of principles-baseddesign rules to determine its waveform characteristics.

[0018] There is a continued need for a device designed to perform aquick and automatic adjustment of phase 2 relative to phase 1 if AEDsare to be advantageously applied to random patients according to a cellresponse model. Further, the model and the device must be adaptable topatient variance and be able to provide automatic adjustment in adynamic environment.

SUMMARY OF THE INVENTION

[0019] The present invention relates to an external defibrillationmethod and apparatus that addresses the limitations in the prior art.The present invention incorporates three singular practices thatdistinguish the practice of designing external defibrillators from thepractice of designing implantable defibrillators. These practices are 1)designing multiphasic transthoracic shock pulse waveforms fromprinciples based on cardiac electrophysiology, 2) designing multiphasictransthoracic shock pulse waveforms in which each phase of the waveformcan be designed without implementation limitations placed on itscharging and delivery means by such means for prior waveform phases, and3) designing multiphasic transthoracic shock pulse waveforms to operateacross a wide range of parameters determined by a large, heterogeneouspopulation of patients.

[0020] In particular, the present invention provides for a method andapparatus for tailoring and reforming a second phase (Ø₂) of a biphasicdefibrillation waveform relative to a first phase (527 ₁) of thewaveform based on intelligent calculations. The method includes thesteps of determining and providing a quantitative description of thedesired cardiac membrane response function. A quantitative model of adefibrillator circuit for producing external defibrillation waveforms isthen provided. Also provided is a quantitative model of a patient whichincludes a chest component, a heart component and a cell membranecomponent. A quantitative description of a transchest externaldefibrillation waveform that will produce the desired cardiac membraneresponse function is then computed. Intelligent calculations based onthe phase 1 cell response is then computed to determine the desiredphase 2 waveform. The computation is made as a function of the desiredcardiac membrane response function, the patient model and thedefibrillator circuit model.

BRIEF DESCRIPTION OF THE DRAWINGS

[0021]FIGS. 1a and 1 b are perspective views of an AED according to thepresent invention.

[0022]FIG. 2a is a very simplified defibrillator model.

[0023]FIG. 2b is a known monophasic defibrillation model.

[0024]FIG. 3 is a known biphasic defibrillation model.

[0025]FIG. 4 represents a monophasic or biphasic capacitive-dischargeexternal defibrillation model according to the present invention.

[0026]FIG. 5a represents a monophasic capacitor-inductor externaldefibrillator model according to the present invention.

[0027]FIG. 5b represents an alternative embodiment of a biphasiccapacitor-inductor external defibrillator model according to the presentinvention.

[0028]FIG. 6 illustrates a biphasic waveform generated utilizing thepresent invention.

[0029]FIG. 7 is a schematic diagram of a circuit which enables theimplementation of the present invention.

[0030]FIG. 8 illustrates a biphasic waveform in relation to a cellularresponse curve.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0031] The present invention provides a method and apparatus fortailoring a second phase ( 2) of a biphasic waveform delivered by anexternal defibrillator, to random patients, by performing intelligentcalculations and analysis to the results of a first phase (4)1) segmentof a biphasic defibrillation waveform and other parameters pertainingthereto. Prior to describing the present invention, a discussion of thedevelopment of an external defibrillation model will be given.

External Defibrillator Model

[0032] The apparatus of the present invention is an automated externaldefibrillator (AED) illustrated in FIGS. 1a and 1 b. FIG. 1a illustratesan AED 10, including a plastic case 12 with a carrying handle 14. A lid16 is provided which covers an electrode compartment 18. An electrodeconnector 20, a speaker 22 and a diagnostic panel (not shown) arelocated on case 12 within electrode compartment 18. FIG. 1b illustratesAED 10 having a pair of electrodes 24 connected thereto. Electrodes 24can be pre-connected to connector 20 and stored in compartment 18.

[0033] The operation of AED 10 is described briefly below. A rescue modeof AED 10 is initiated when lid 16 is opened to access electrodes 24.The opening of lid 16 is detected by AED 10 to effectively turn on thedevice. AED 10 then quickly runs a short test routine. After electrodes24 have been placed on the patient, AED 10 senses patient specificparameters, such as impedance, voltage, current, charge or othermeasurable parameters of the patient. The patient specific parametersare then utilized in the design of optimal waveforms as will bedescribed below.

[0034] If a shockable condition is detected through electrodes 24, aplurality of capacitors inside of AED 10 are charged from an energysource, typically a detachable battery pack. Based upon the patientspecific parameters sensed, the duration and other characteristics of adischarge waveform are then calculated. The energy stored in AED 10 isthen discharged to the patient through electrodes 24.

[0035] For a more detailed description of the physical structure of AED10 or the process involved in sensing, charging, shocking and testing,reference should be made to Applicant's issued U.S. Pat. No. 5,645,571,which is assigned to the assignee of the present invention, thedisclosure of which is herein incorporated by reference.

[0036] In the present invention it is not assumed that both phases of abiphasic waveform are delivered using the same set of capacitors or thatboth phases of a biphasic waveform are delivered using the capacitor setin the same electrical configuration, although such an embodiment isconsidered within the spirit and scope of the present invention.

[0037] Transthoracic defibrillation is generally performed by placingelectrodes on the apex and anterior positions of the chest wall. Withthis electrode arrangement, nearly all current passing through the heartis conducted by the lungs and the equipotential surfaces pass throughthe myocardium normal to the electrode axis. The present invention usesthe transthoracic charge burping model to develop design equations thatdescribe the time course of a cell's membrane potential during atransthoracic biphasic shock pulse. These equations are then used tocreate equations that describe the design of monophasic and biphasicshock pulses for transchest defibrillation to optimize the design of Ø₁for defibrillating and the design of Ø₂ for stabilizing. Theseoptimizing shock pulse design equations are called design rules.

[0038] According to the present invention, the main series pathway forcurrent is to pass through the chest wall, the lungs, and the heart.Additionally, there are two important shunting pathways in parallel withthe current pathway through the heart. These shunting pathways must betaken into consideration. The lungs shunt current around the heartthrough a parallel pathway. The second shunting pathway is provided bythe thoracic cage. The resistivity of the thoracic cage and the skeletalmuscle structure is low when compared to lungs. The high resistivity ofthe lungs and the shunting pathways are characterizing elements ofexternal defibrillation that distinguish the art from intracardiacdefibrillation and implantable defibrillation technologies.

[0039] Therefore, in the transthoracic defibrillation model of thepresent invention illustrated in FIG. 4, there are several resistancesin addition to those discussed for the charge burping model above. R_(S)represents the resistance of the defibrillation system, including theresistance of the defibrillation electrodes. R_(CW) and R_(TC) representthe resistances of the chest wall and the lungs, respectively, in serieswith resistance of the heart, R_(H). R_(TC) and R_(LP) represent theresistances of the thoracic cage and the lungs, respectively, inparallel with the resistance of the heart.

[0040] The design rules for external defibrillation waveforms aredetermined in three steps. In the first step, the transchest forcingfunction is determined. The transchest forcing function is the name thatis given to the voltage that is applied across each cardiac cell duringan external defibrillation shock. In the second step, the designequations for Ø₁ of a shock pulse are determined. The design equationsare the equations describing the cell's response to the Ø₁ transchestforcing function, the equation describing the optimal Ø₁ pulse duration,and the equation describing the optimal Ø₁ capacitor. Therefore, steptwo relates the cell response to the action of a monophasic shock pulseor the first phase of a biphasic shock pulse. This relation is used todetermine the optimal design rules and thereby design parameters for theimplementation of this phase in an external defibrillator. It will beclear to those in the art that step two is not restricted to capacitordischarge shock pulses and their associated transchest forcing function.Another common implementation of an external defibrillator incorporatesa damped sine wave for a shock pulse and can be either a monophasic orbiphasic waveform. This type of external defibrillator is modeled by thecircuits shown in FIGS. 5a and 5 b. In the third step, the designequations for Ø₂ of a shock pulse are determined. The design equationsare the equations describing the cell's response to the Ø₂ transchestforcing function, the equation describing the optimal Ø₂ pulse durationand the equation describing the optimal Ø₂ capacitor. These designequations are employed to determine the optimal design rules and therebydesign parameters of Ø₂ of a biphasic shock pulse with respect to howthe cell responds to the shock pulse. An important element of thisinvention is to provide shock pulse waveforms that are designed from acardiac cell response model developed from first principles and thatcorrectly determines the effects of the chest and its components on theability of a shock pulse to defibrillate.

[0041] The transchest forcing function is determined by solving for thevoltage found at node V₃ in FIG. 4. The transchest forcing function isderived by solving for V₃ using the following three nodal equations:$\begin{matrix}{{{\frac{V_{1} - V_{S}}{R_{S}} + \frac{V_{1}}{R_{TC}} + \frac{V_{1} - V_{2}}{R_{CW}}} = 0},} & (1) \\{{{\frac{V_{2} - V_{1}}{R_{CW}} + \frac{V_{2}}{R_{LP}} + \frac{V_{2} - V_{3}}{R_{LS}}} = 0},\quad {and}} & (2) \\{{\frac{V_{3} - V_{2}}{R_{LS}} + \frac{V_{3}}{R_{H}} + \frac{V_{3} - V_{M}}{R_{M}}} = 0.} & (3)\end{matrix}$

[0042] Equation 1 can be rewritten as $\begin{matrix}{{V_{1}\left( {\frac{1}{R_{S}} + \frac{1}{R_{TC}} + \frac{1}{R_{CW}}} \right)} = {\frac{V_{S}}{R_{S}} + {\frac{V_{2}}{R_{CW}}.}}} & \text{(4A)} \\{{V_{1} = {\frac{V_{S}}{R_{S}\Omega_{1}} + \frac{V_{2}}{R_{CW}\Omega_{1}}}},{{{where}\quad \Omega_{1}} = {\frac{1}{R_{S}} + \frac{1}{R_{TC}} + {\frac{1}{R_{CW}}.}}}} & \text{(4B)}\end{matrix}$

$\begin{matrix}{{V_{2}\left( {\frac{1}{R_{CW}} + \frac{1}{R_{LP}} + \frac{1}{R_{LS}}} \right)} = {\frac{V_{1}}{R_{CW}} + \frac{V_{3}}{R_{LS}}}} & \text{(4C)}\end{matrix}$

[0043] By substituting equation 4B for V₁ into equation 4C, we can solvefor V₂ as an expression of V_(S) and V₃: $\begin{matrix}\begin{matrix}{{V_{2} = {\frac{V_{S}}{R_{S}R_{C}\Omega_{1}\Omega_{2}\Omega_{22}} + \frac{V_{3}}{R_{LS}\Omega_{2}\Omega_{22}}}},{where}} \\{{\Omega_{2} = {\frac{1}{R_{LS}} + \frac{1}{R_{LP}} + \frac{1}{R_{CW}}}},{and}} \\{\Omega_{22} = {1 - {\frac{1}{R_{CW}^{2}\Omega_{1}\Omega_{2}}.}}}\end{matrix} & (5)\end{matrix}$

[0044] Now solving for V₃ as an expression of V_(S) and V_(M), equation3 may be re-arranged as $\begin{matrix}{{V_{3}\left( {\frac{1}{R_{LS}} + \frac{1}{R_{H}} + \frac{1}{R_{M}}} \right)} = {\frac{V_{2}}{R_{LS}} + \frac{V_{M}}{R_{M}}}} & (6)\end{matrix}$

[0045] so that $\begin{matrix}{V_{3} = {{\frac{V_{2}}{R_{LS}\Omega_{3}} + {\frac{V_{M}}{R_{M}\Omega_{3}}\quad {where}\quad \Omega_{3}}} = {\frac{1}{R_{LS}} + \frac{1}{R_{H}} + {\frac{1}{R_{M}}.}}}} & (7)\end{matrix}$

[0046] Substituting equation 5 for V₂ into equation 7, we can solve forV₃ as an expression of V_(S) and V_(M): $\begin{matrix}{V_{3} = {\frac{V_{S}}{R_{S}R_{CW}R_{LS}\Omega_{1}\Omega_{2}\Omega_{22}\Omega_{3}\Omega_{33}} + {\frac{V_{M}}{R_{M}\Omega_{3}\Omega_{33}}\quad {where}}}} & (8) \\{\Omega_{33} = {1 - \frac{1}{\left( {R_{LS}^{2}\Omega_{2}\Omega_{22}\Omega_{3}} \right)}}} & (9)\end{matrix}$

[0047] From equation 8 we define Ω_(M) to be: $\begin{matrix}\begin{matrix}{\Omega_{M} = {{R_{M}\Omega_{3}\Omega_{33}} = {R_{M}{\Omega_{3}\left( {1 - \frac{1}{\left( {R_{LS}^{2}\Omega_{2}\Omega_{22}\Omega_{3}} \right)}} \right)}}}} \\{\Omega_{M} = {R_{M}\left( {\Omega_{3} - \frac{1}{R_{LS}^{2}\left( {\Omega_{2} - \frac{1}{R_{CW}^{2}\Omega_{1}}} \right)}} \right)}}\end{matrix} & (10)\end{matrix}$

[0048] From equation 8 we also define Q S to be:

Ω_(S)=R_(S)R_(CW)R_(LS)Ω₁Ω₂Ω₃Ω₂₂Ω₃₃   (11)

[0049] $\begin{matrix}{\Omega_{S} = {R_{S}R_{CW}R_{LS}\Omega_{1}{\Omega_{2}\left( {1 - \frac{1}{\left( {R_{CW}^{2}\Omega_{1}\Omega_{2}} \right)}} \right)}{\Omega_{3}\left( {1 - \frac{1}{\left( {R_{LS}^{2}\Omega_{2}\Omega_{22}\Omega_{3}} \right)}} \right)}}} & (12) \\{\Omega_{S} = {R_{S}R_{CW}{R_{LS}\left( {{\Omega_{1}\Omega_{2}} - \frac{1}{R_{CW}^{2}}} \right)}\left( {\Omega_{3} - \frac{1}{R_{LS}^{2}\left( {\Omega_{2} - \frac{1}{R_{CW}^{2}\Omega_{1}}} \right)}} \right)}} & (13) \\{{{so}\quad {that}\quad V_{3}} = {\frac{V_{S}}{\Omega_{S}} + \frac{V_{M}}{\Omega_{M}}}} & (14)\end{matrix}$

[0050] is the general transchest transfer function as shown in FIG. 4 orFIGS. 5a and 5 b. Equation 14 encapsulates the transchest elements andtheir association between the forcing function V_(S) (which models adefibrillation circuit and the shock pulse) and the cell membranevoltage V_(M). Therefore, this completes the first step.

[0051] The variable V_(S) may now be replaced with a more specificdescription of the defibrillation circuitry that implements a shockpulse. For a first example, a monophasic time-truncated,capacitive-discharge circuit may be represented by V_(S)=V₁e^(−t/τ) ₁,where V₁ is the leading-edge voltage for the shock pulse and τ₁=RC₁,with R determined below.

[0052] As shown in FIGS. 5a and 5b, a second example would be amonophasic damped sine wave circuit, represented by $\begin{matrix}{V_{S} = {{V_{1}\left( \frac{\tau_{C1}}{\tau_{C1} - {\tau \quad}_{L1}} \right)}\left( {e^{{- t}/\tau_{C1}} - e^{{- t}/\tau_{L1}}} \right)}} & \text{(14B)}\end{matrix}$

[0053] where V₁ is the voltage on the charged capacitor C₁,τ_(C1)=R_(C1) and τ_(L1)=L₁/R. Every step illustrated below may beperformed with this and other similar transchest forcing functions whichrepresent defibrillator circuitry.

[0054] To proceed with step two, from FIG. 4, nodal analysis provides anequation for VM_(M): $\begin{matrix}{{{C_{M}\frac{V_{M}}{t}} + \frac{V_{M} - V_{3}}{R_{M}}} = 0.} & (15)\end{matrix}$

[0055] Rearranging equation 15, we have $\begin{matrix}{{{C_{M}\frac{V_{M}}{t}} + \frac{V_{M}}{R_{M}}} = {\frac{V_{3}}{R_{M}}.}} & (16)\end{matrix}$

[0056] Next, substituting equation 14 as an expression for V₃ intoequation 16, the cell membrane response is now calculated as follows:$\begin{matrix}{{{C_{M}\frac{V_{M}}{t}} + \frac{V_{M}}{R_{M}}} = {\frac{1}{R_{M}}\left( {\frac{V_{S}}{\Omega_{S}} + \frac{V_{M}}{\Omega_{M}}} \right)}} & (17) \\{{{C_{M}\frac{V_{M}}{t}} + \frac{V_{M}}{R_{M}} - \frac{V_{M}}{R_{M}\Omega_{M}}} = {{{\frac{V_{S}}{R_{M}\Omega_{M}}C_{M}\frac{V_{M}}{t}} + {\frac{V_{M}}{R_{M}}\left( {1 - \frac{1}{\Omega_{M}}} \right)}} = \frac{V_{S}}{R_{M}\Omega_{S}}}} & (18)\end{matrix}$

[0057] Dividing through by C_(M), and setting τ_(M)=R_(M)C_(M), thenequation 18 becomes $\begin{matrix}{{\frac{V_{M}}{t} + {\frac{V_{M}}{\tau_{M}}\left( {1 - \frac{1}{\Omega_{M}}} \right)}} = {\frac{V_{S}}{\tau_{M}}{\left( \frac{1}{\Omega_{S}} \right).}}} & (19)\end{matrix}$

[0058] Equation 19 is a general ordinary differential equation (ODE)that models the effects of any general forcing function V_(S) thatrepresents a phase of a shock pulse waveform applied across the chest.The general ODE equation 19 models the effects of a general shock pulsephase V_(S) on the myocardium, determining cardiac cell response to sucha shock pulse phase.

[0059] In the equations given below:

[0060] C₁ equals the capacitance of the first capacitor bank andV_(S)=V₁e^(−t/τ) ₁;

[0061] C₂ equals the capacitance of the second capacitor bank andV_(S)=V₂e^(−t/τ) ₂;

[0062] R=R_(S)+R_(B), where R_(S)=System impedance (device andelectrodes);

[0063] R_(B)=body impedance (thoracic cage, chest wall, lungs (series,parallel), heart).

[0064] To determine body impedance, R_(B), we see that the seriescombination of R_(H) and R_(LS) yields R_(H)+R_(LS). (FIG. 4). Theparallel combination of R_(H)+R_(LS) and R_(LP) yields: $\begin{matrix}{\frac{R_{LP}\left( {R_{LS} + R_{H}} \right)}{R_{LP} + R_{LS} + R_{H}}.} & (20)\end{matrix}$

[0065] The series combination of equation 20 and R_(CW) yields:$\begin{matrix}{R_{CW} + {\frac{R_{LP}\left( {R_{LS} + R_{H}} \right)}{\left( {R_{LP} + R_{LS} + R_{H}} \right)}.}} & (21)\end{matrix}$

[0066] The parallel combination of equation 21 and R_(TC) yields:$\begin{matrix}{R_{B} = \left\lbrack \frac{{R_{TC}R_{CW}} + \frac{R_{LP}\left( {R_{LS} + R_{H}} \right)}{\left( {R_{LP} + R_{LS} + R_{H}} \right)}}{R_{TC} + R_{CW} + \frac{R_{LP}\left( {R_{LS} + R_{H}} \right)}{\left( {R_{LP} + R_{LS} + R_{H}} \right)}} \right\rbrack} & (22)\end{matrix}$

[0067] where R_(B) is the impedance of the body for this model.

[0068] The discharge of a single capacitor is modeled by V_(S)=V₁e^(−t/τ) ₁ for an initial C₁ capacitor voltage of V₁. Placing V_(S)into equation 19 gives: $\begin{matrix}{{\frac{V_{M}}{t} + {\frac{V_{M}}{\tau_{M}}\left( {1 - \frac{1}{\Omega_{M}}} \right)}} = \frac{V_{1}^{{- t}/\tau_{1}}}{\tau_{M}\Omega_{S}}} & (23)\end{matrix}$

[0069] where τ_(M)=R_(M)C_(M) represents the time constant of themyocardial cell in the circuit model, and τ₁, which equals R_(S)C₁,represents the time constant of Ø₁. Such a standard linear ODE asequation 23 has the form ${\frac{y}{x} + {{P(X)}Y}} = {{Q(x)}.}$

[0070] These linear ODEs have an integration factor that equalse^(∫pdx). The general solution to such equations is:

y=e^(∫pdx)[∫e^(∫pdx)Qdx+c]

[0071] The ODE in equation 23 models the effects of each phase of atime-truncated, capacitor-discharged shock pulse waveform. Equation 23is a first-order linear ODE, and may be solved using the method ofintegration factors, to get: $\begin{matrix}{{V_{M1}(t)} = {{k\quad ^{{- {({t/\tau_{M}})}}{({1 - \frac{1}{\Omega_{M}}}}}} + {\left( \frac{V_{1}}{\Omega_{S}} \right)\left( \frac{\tau_{1}}{{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right){^{{- t}/\tau_{M}}.}}}} & (24)\end{matrix}$

[0072] Equation 24 is an expression of cell membrane potential during Ø₁of a shock pulse. To determine the constant of integration k, theinitial value of V_(M1) is assumed to be V_(M1)(0)=V_(G) (“cellground”). Applying this initial condition to equation 24, k is found tobe $\begin{matrix}{k = {V_{G} - {\left( \frac{V_{o}}{\Omega_{S}} \right){\left( \frac{\tau_{1}}{{\tau_{1}\left( {1 - \frac{1}{M}} \right)} - \tau_{M}} \right).}}}} & (25)\end{matrix}$

[0073] Assuming τ₁=RC₁, where R=R_(S)+R_(B), then the solution to theinitial-value problem for Ø₁ is: $\begin{matrix}\begin{matrix}{{V_{M1}(t)} = \quad {V_{G^{e}} - {\left( {t/\tau_{M}} \right)\left( {1 - \frac{1}{\Omega_{M}}} \right)} + {\left( \frac{V_{1}}{\Omega_{S}} \right)\left( \frac{\tau_{1}}{{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right)}}} \\{\quad \left( {^{{- t}/\tau_{1}} - ^{{- {({t/\tau_{M}})}}{({1 - \frac{1}{\Omega_{M}}})}}} \right)}\end{matrix} & (26)\end{matrix}$

[0074] Equation 26 describes the residual voltage found on a cell at theend of Ø₁.

[0075] Assuming V_(G)=0 and V₁=1, the solution for cell response to anexternal shock pulse is $\begin{matrix}{{V_{M1}(t)} = {\left( \frac{1}{\Omega_{S}} \right)\left( \frac{\tau_{1}}{{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right){\left( {^{\frac{- t}{\tau_{1}}} - ^{{- {(\frac{t}{\tau_{M}})}}{({1 - \frac{1}{\Omega_{M}}})}}} \right).}}} & (27)\end{matrix}$

[0076] We may now determine optimal durations for Ø₁ according tocriteria for desired cell response. One such design role or criterion isthat the Ø₁ duration is equal to the time required for the externaldefibrillator shock pulse to bring the cell response to its maximumpossible level. To determine this duration, equation 27 isdifferentiated and the resulting equation 27B is set to zero. Equation27B is then solved for the time t, which represents shock pulse durationrequired to maximize cardiac cell response. $\begin{matrix}{{{{{\left( \frac{AB}{\tau_{M}} \right)^{{- {Bt}}/\tau_{M}}} - {\left( \frac{A}{\tau_{1}} \right)^{{- t}/\tau_{1}}}} = 0},{{{where}\quad A} = {\left( \frac{1}{\Omega_{S}} \right)\left( \frac{\tau_{1}}{{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right)\quad {and}}}}\text{}\quad {B = {1 - {\frac{1}{\Omega_{M}}.}}}} & \text{(27B)}\end{matrix}$

[0077] Solving for t, the optimal duration d Ø₁ for a monophasic shockpulse or Ø₁ of a biphasic shock pulse is found to be $\begin{matrix}{{{d\quad \varphi_{1}} = {\left( \frac{\tau_{1}\tau_{M}}{{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right){\ln\left( \frac{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)}{\tau_{M}} \right)}}},} & \text{(27C)}\end{matrix}$

[0078] where “1n” represents the logarithm to the base e, the naturallogarithm.

[0079] For Ø₂, an analysis almost identical to equations 20 through 27above is derived. The differences are two-fold. First, a biphasicwaveform reverses the flow of current through the myocardium during Ø₂.Reversing the flow of current in the circuit model changes the sign onthe current. The sign changes on the right hand side of equation 23.

[0080] The second difference is the step taken to incorporate anindependentØ₂ into the charge burping model. Therefore, the Ø₂ ODEincorporates the C₂ capacitor set and their associated leading-edgevoltage, V₂, for the Ø₂ portion of the pulse. Then τ₂ represents the Ø₂time constant; τ₂=RC₂, and V_(S)=−V₂e^(−t/τ) ₂. Equation 23 now becomes:$\begin{matrix}{{\frac{V_{M}}{t} + {\left( \frac{V_{M}}{\tau_{M}} \right)\left( {1 - \frac{1}{\Omega_{M}}} \right)}} = {\frac{{- V_{2}}^{{- t}/\tau_{2}}}{\tau_{M}\Omega_{M}}.}} & (29)\end{matrix}$

[0081] Equation 29 is again a first-order linear ODE. In a similarmanner, its general solution is determined to be: $\begin{matrix}{{V_{M2}(t)} = {{k\quad ^{{({{- t}/\tau_{M}})}{({1 - \frac{1}{\Omega_{M}}})}}} - {\left( \frac{V_{2}}{\Omega_{S}} \right){\left( \frac{\tau_{2}}{{\tau_{2}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right).}}}} & (30)\end{matrix}$

[0082] To determine the constant of integration k, the value of V_(M2)at the end of Ø₁ is

V_(M2)(0)=V_(M1)(d_(Ø1))=V_(Ø1),   (31)

[0083] where d Ø₁ is the overall time of discharge for Ø₁ and V_(Ø1) isthe voltage left on the cell at the end of Ø₁. Applying the initialcondition to equation 30 and solving for k: $\begin{matrix}{k = {V_{\varphi 1} + {\left( \frac{V_{2}}{\Omega_{S}} \right){\left( \frac{\tau_{2}}{{\tau_{2}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right).}}}} & (32)\end{matrix}$

[0084] The solution to the initial-value problem for Ø₂ is$\begin{matrix}\begin{matrix}{{V_{M2}(t)} = \quad {{\left( \frac{V_{2}}{\Omega_{S}} \right)\left( \frac{\tau_{2}}{{\tau_{2}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right)\left( {^{{- {({t/\tau_{M}})}}{({1 - \frac{1}{\Omega_{M}}})}} - ^{{- t}/\tau_{2}}} \right)} +}} \\{\quad {V_{\varphi 1}{^{{- {({t/\tau_{M}})}}{({1 - \frac{1}{\Omega_{M}}})}}.}}}\end{matrix} & (33)\end{matrix}$

[0085] Equation 33 provides a means to calculate the residual membranepotential at the end of Ø₂ for the cells that were not stimulated by Ø₁.Setting Equation 3 3 equal to zero, we solve for t, thereby determiningthe duration of Ø₂, denoted dØ₂, such that V_(M2)(dØ₂)=0. By designingØ₂ with a duration d Ø₂, the biphasic shock pulse removes the residualchange placed on a cell by Ø₁. We determine d Ø₂ to be: $\begin{matrix}\begin{matrix}{d_{\varphi 2} = \quad {\left( \frac{\tau_{2}\tau_{M}}{{\tau_{2}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right) \cdot {\ln\left( {1 +} \right.}}} \\{\quad {\left( \frac{{\tau_{2}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}}{\tau_{2}} \right)\left( \frac{\Omega_{S}V_{\varphi 1}}{V_{2}} \right){).}}}\end{matrix} & (34)\end{matrix}$

[0086] From the equations above, an optimal monophasic or biphasicdefibrillation waveform may be calculated for an external defibrillator.Then the table below illustrates the application of the design rule asthe overall chest resistance ranges from 25 Ω to 200 Ω: R (Ω) τ₁ dφ₁)V_(final) E_(delivered) 25  5.2 5.05  757 343 50 10.2 6.90 1017 297 7515.2 8.15 1170 263 100 20.2 9.10 1275 238 125 25.2 9.90 1350 216 15030.2 10.55 1410 201 175 35.2 11.15 1457 186 200 40.2 11.65 1497 176

[0087] It should be noted and understood that the design of Ø₂ isindependent from Ø₁. To design Ø₂, the only information necessary fromØ₁ is where the cell response was left when Ø₁ was truncated.Additionally, Ø₂ need not use the same or similar circuitry as that usedfor Ø₁. For example, Ø may use circuitry as illustrated in FIG. 4 whereØ₂ may use circuitry illustrated in FIG. 5a, or vice-versa. Thecorresponding design rules for a Ø₁ circuitry may be used in conjunctionwith the design rules for a Ø₂ circuitry, regardless of the specificcircuitry used to implement each phase of a monophasic or biphasic shockpulse.

PRESENT INVENTION

[0088] The present invention is based on the charge burping modelhypothesis which postulates and defines an optimal pulse duration for Ø₂as a duration that removes as much of the Ø₁ residual charge from thecell as possible. Ideally, the objective is to maintain unstimulatedcells with no charge or set them back to relative ground.

[0089] A further objective of the present invention is to formulate ameasurement by which the optimal duration of τ_(S) (cell time constant)and τ_(M) (membrane time constant) can be measured. Although one canchoose a proper Ø₂ (fixed) for a given cell response Ø₁, intransthoracic shock pulse applications, τ_(M) is not known and it variesacross patients, waveforms and time. For a fixed Ø₂, therefore, theerror in τ_(M) could be substantial. Realizing this, the presentinvention is designed to correct for “range” of candidate τ_(M) valuesto fit an optimal duration for a fixed Ø₂. In other words, Ø₂ isselected so that the capacitance in the model is matched with measuredR_(H) to get a “soft landing” to thereby minimize error due to τ_(M)±Ein charge burping ability of Ø₂ involving patient variability.

[0090] The technique of “soft landing” advanced by the present inventionlimits the error in τ_(M) and sets Ø₂ to dynamically adjust within arange of possible τ_(M) values. As discussed hereinbelow, optimizingsolutions are used to determine parameters on which intelligentcalculations could be made so that autonomous Ø₂ adjustments forvariable R_(H) are possible.

[0091] The charge burping model also accounts for removing the residualcharge at the end of Ø₁ based on Ø₂ delivered by a separate set ofcapacitors other than those used to deliver Ø₁.

[0092] Referring now to FIG. 3, Cl represents the Ø₁ capacitor set andC₂ represents the Ø₂ capacitor, R_(H) represents the resistance of theheart, and the pair C_(M) and R_(M) represent the membrane seriescapacitance and resistance of a single cell. The node V_(S) representsthe voltage between the electrodes, while V_(M) denotes the voltageacross the cell membrane.

[0093] Accordingly, one of the advantages that AEDs have over ICDs, isthat the implementation of a Ø₂ waveform may be completely independentof the implementation of Ø₁. Specifically, the charging and dischargingcircuits for Ø₁ and Ø₂ do not need to be the same circuitry. UnlikeICDs, AEDs are not strictly constrained by space and volumerequirements. Within practical limits, in AEDs the capacitance andvoltage which characterize Ø₂ need not depend on the circuitry and thevalues of Ø₁.

[0094] The Lerman-Deale model for AEDs define the main series forcurrent to pass through the chest wall, the lungs and the heart.Further, two shunting pathways in parallel with current pathway throughthe heart are defined. Another shunting pathway is provided by thethoracic cage. However, when compared to the resistivity of the lungs,the thoracic cage resistance is rather negligible.

[0095] Thus, considering the transthoracic defibrillation model of FIG.4, there are several other resistances in addition to those discussedfor the charge burping model hereinabove. R_(S) represents theresistance of the defibrillation system, including the resistance of theelectrodes. R_(CW) and R_(LS) represent the resistances of the chestwall and the lungs, respectively, in series with resistance of theheart, R_(H). R_(TC) and R_(LP) represent the resistances of thethoracic cage and the lungs, respectively, in parallel with theresistance of the heart.

[0096] As discussed hereinabove, developing design equations whichenable adjustments for variable resistances encountered in thetransthoracic defibrillation model of FIG. 4 is one of the advances ofthe present invention. In order to adjust for variable R_(H) both Ø₁ andØ₂ are assumed fixed. Then Ø₂ is selected to have a range of capacitancevalues which permit to optimize the slope of the voltage curve at timet. In other words, C_(S2) for Ø₂ is chosen such that {fraction(dv/dt)}=0 The design parameters of the present invention are derivedfrom equation 35, as follows:

V_(M)(t)=V_(O)(1−e^(−t/τM).)   (35)

[0097] Equation 35 can be rewritten as: $\begin{matrix}\begin{matrix}{{V_{M2}(t)} = \quad {{{\left( {V_{\varphi 1} + {\left\{ \frac{\tau_{2}}{\tau_{2} - \tau_{M}} \right\} V_{2}}} \right)} - \frac{\tau}{\tau_{M}}} -}} \\{\quad {{\left\{ \frac{\tau_{2}}{\tau_{M} - \tau_{M}} \right\} V_{2}^{{- t}/\tau_{2}}} = 0.}}\end{matrix} & (36)\end{matrix}$

[0098] Letting${A = {{V_{\varphi 1} + {B\quad {and}\quad B}} = {\frac{\tau_{2}}{\tau_{2} - \tau_{M}}V_{2}}}},$

[0099] equation 36 can be written as: $\begin{matrix}{{V(t)} = {{A\quad } - \frac{t}{\tau_{M}} - {B\quad {\frac{- t}{\tau_{2}}.}}}} & (37)\end{matrix}$

[0100] Differentiating equation 37 with respect to t, we have thefollowing: $\begin{matrix}{\frac{v}{t} = {{{- \frac{A\quad ^{- {t\tau}_{M}}}{\tau_{M}}} + {\frac{B}{\tau_{M}}^{{- t}/\tau_{2}}}} = 0.}} & (38)\end{matrix}$

[0101] Equation 38 is the profile of Ø₁ waveform and at${\frac{v}{t} = 0},$

[0102] the slope of the curve is zero, which means the terminal value ofthe time constant is determinable at this point. Thus, solving equation38 for the value of t, we have: $\begin{matrix}{t = {{\frac{\tau_{2}\tau_{M}}{\tau_{2} - \tau_{M}} \cdot \ln}\left\{ {\frac{\tau_{2}}{\tau_{M}}\frac{\left( {V_{\varphi 1} + {\frac{\tau_{2}}{\tau_{2} - \tau_{M}}V_{2}}} \right)}{\left( \frac{\tau_{2}}{\tau_{2} - \tau_{M}} \right)V_{2}}} \right\}}} & (39)\end{matrix}$

[0103] where $\begin{matrix}{t_{1} = {\left( \frac{\tau_{2}\tau_{M}}{\tau_{2} - \tau_{M}} \right)\ln \left\{ {1 + {\left( \frac{\tau_{2}\tau_{M}}{\tau_{2}} \right)\left( \frac{V_{\varphi 1}}{V_{2}} \right)}} \right\}}} & (40) \\{t_{1} = {t_{1} + {\left( {\frac{\tau_{2}\tau_{M}}{\tau_{2} - \tau_{M}}\ln \left\{ \frac{\tau_{2}}{\tau_{M}} \right\}} \right).}}} & (41)\end{matrix}$

[0104] For biphasic defibrillation waveforms, it is generally acceptedthat the ratio of Ø₁ duration (τ_(M)) to Ø₂ duration Ø₂ should be >1.Charge burping theory postulates that the beneficial effects of Ø₂ aremaximal when it completely removes the charge deposited on myocardialcell by Ø₁. This theory predicts that Ø₁/Ø₂ should be >1 when τ_(S)is >3 τ_(S) and <1 when τ_(S)<3 ms. τ_(S) is defined as the product ofthe pathway resistance and capacitance. (See NASPE ABSTRACTS, Section361 entitled Charge Buriing Predicts Optimal Ratios of Phase Durationfor Biphasic Defibrillation, by Charles D. Swerdlow, M.D., Wei Fan,M.D., James E. Brewer, M. S., Cedar-Sinai Medical Center, Los Angeles,Calif.

[0105] In light of the proposed duration ratio of Ø₁ and Ø₂, wherein theoptimal solution is indicated to be at t₁=t₂ where t is the duration ofØ₁ and t₂ is the duration of Ø₂ and superimposing this condition onequation 41 hereinabove, we have:${t_{2} = {{t_{1} + {\left( {{\frac{\tau_{2}\tau_{M}}{\tau_{2} - \tau_{M}} \cdot \ln}\left\{ \frac{\tau_{2}}{\tau_{M}} \right\}} \right)\quad {setting}\quad t_{2}}} = t_{1}}},$

[0106] remanaging terms we have: $\begin{matrix}\begin{matrix}{{t_{2} - t_{1}} = \quad {0 = {{\frac{\tau_{2}\tau_{M}}{\tau_{2} - \tau_{M}} \cdot \ln}\left\{ \frac{\tau_{2}}{\tau_{M}} \right\} \quad {or}\quad \tau_{2}{\tau_{M} \cdot}}}} \\{\quad {{\ln \left\{ \frac{\tau_{2}}{\tau_{M}} \right\} \quad {or}\quad \ln \quad \frac{\tau_{2}}{\tau_{M}}} = {{0\quad {or}\quad \frac{\tau_{2}}{\tau_{M}}} = 1.}}}\end{matrix} & (42)\end{matrix}$

[0107] From the result of equation 42 we make the final conclusion thatthe optimal charge burping is obtained when t₂=t_(M). From priordefinition, we have established that t_(M)=R_(H) C_(S). Thus, inaccordance with equation 42, t₂=t_(M)=R_(H). C_(S).

[0108] Referring now to FIG. 6, a biphasic defibrillation waveformgenerated using the equations 35-42 is shown. At V_(M)=0 anddV_(M)/dt=0, Ø₁ and Ø₂ are equal to zero.

[0109]FIG. 7 is a schematic of a circuit which enables theimplementation of the theory developed in the present invention. Thecircuit shows a plurality of double throw switches connecting aplurality of capacitors. The capacitors and the switches are connectedto a charge or potential source. The voltage is discharged viaelectrodes. One aspect of implementing the “soft landing” charge burpingtechnique developed in the present invention is to fix C_(S) for Ø₁ andfix C_(S) for Ø₂. Further, t_(M) is fixed. Then a range of resistancevalues representing R_(H) are selected. The t_(M) and R_(H) rangesrepresent the patient variability problem. The objective is to enablecorrective action such that C_(S) values could range between 40 uf-200uf and dv/dt=0 for t₂. As indicated hereinabove, the error in chargeburping is minimized for t₂ when dv/dt=0.

[0110] The implementation of the present invention requires thatcapacitor bank values be determined for Ø₁ and Ø₂. Specifically, thecapacitor values for Ø₁ should be designed to realize dv/dt =0 and V=0for Ø₂ to minimize charge burping error due to R_(H) and t_(M). Where avariable resistor is used to set R_(H) thus providing a known butvariable value and t_(M) can be set within these practical ranges.

[0111]FIG. 8 depicts a biphasic defibrillation waveform 300, generatedusing equations 35-42 above, in relation to a predicted patient'scellular response curve 304; the cellular response, as explained earlieris based on a patient's measured impedance. As shown, the residualcharge left on the cardiac cells after delivery of Ø₁ has been broughtback to zero charge, i.e., charge balanced, after the delivery of Ø₂.This charge balance has been achieved because the energy delivered hasbeen allowed to vary.

[0112] Traditionally, all defibrillation waveforms have delivered afixed energy. This has been primarily because therapy has been measuredin joules. These fixed energy waveforms, which include monophasic dampedsine, biphasic truncated exponential, and monophasic truncatedexponential waveforms, only passively responded to patient and/or systemimpedance.

[0113] This passive response was by charging a capacitor to a fixedvoltage, wherein the voltage was adjusted depending on amount of fixedenergy to be delivered that was desired, and discharging it across thepatient, whom acts as the load. The energy delivered is controlled bythe simple equation: $\begin{matrix}{E = {\frac{1}{2}{CV}^{2}}} & (43)\end{matrix}$

[0114] where: E is the energy, C is the capacitance of the chargingcapacitor, and V is the voltage.

[0115] In the case of the truncated exponential waveform, equation 43 isextended to: $\begin{matrix}{E = {\frac{1}{2}{C\left( {V_{i}^{2} - V_{f}^{2}} \right)}}} & (44)\end{matrix}$

[0116] where: V_(i) is the initial voltage and V_(f) is the finalvoltage.

[0117] Significantly, no form of patient impedance or system impedanceappears in either of the above equations.

[0118] With respect to system impedance, the above equations make theassumption that the internal impedance of the defibrillator is 0 ohms.This is a good approximation for truncated exponential waveforms, but itis not a good approximation for damped sine waveforms. Damped sinewaveforms typically have 10-13 ohms internal impedance. This internalimpedance effects the delivered energy. The internal impedance of thedefibrillator will absorb a portion of the stored energy in thecapacitor, thus reducing the delivered energy. For low patientimpedances, the absorbed energy can become quite significant, with onthe order of 40% of the stored energy being absorbed by the internalresistances.

[0119] With respect to patient impedance, the patient acts as the loadand, as such, the peak current is simply a function of the peak voltagevia Ohm's law: $\begin{matrix}{I = \frac{V}{R}} & (45)\end{matrix}$

[0120] where: I is the current and R represents the patient's impedance.

[0121] As equation 45 indicates, the current is inversely proportionalto the impedance. This means that there is lower current flow for highimpedance patients which, in turn, means that it takes longer to deliverthe energy to a high impedance patient. This fact is further exemplifiedwhen considering the equation for a truncated exponential voltage at anypoint in time: $\begin{matrix}{{V(t)} = {\frac{1}{2}{CV}_{i}e^{- \frac{t}{RC}}}} & (46)\end{matrix}$

[0122] Equation 46 shows that patient impedance, R, is reflected withinin the voltage equation which forms a part of the energy equation.Equation 46 shows that the duration of a defibrillation waveform extendspassively with impedance, since it takes longer to reach the truncatevoltage.

[0123] To actively respond to system and patient impedances, as thepresent invention does with its charge burping model, the energy or thevoltage must be allowed to vary. However, there is a problem withvarying the voltage in that the voltage is set before energy delivery.Thus, making the voltage the more difficult variable to manage. On theother hand, energy may be adjusted on the fly, making it the easiervariable to manage. To explain further, in the charge balance waveformof the present invention, there is a desire to exactly terminate thedefibrillation waveform when the cellular response curve returns to zerocharge, see again FIG. 8 Failing to terminate the defibrillationwaveform when the cellular response curve returns to zero charge, e.g.,overshooting or undershooting the neutral condition, can promoterefibrillation.

[0124] In achieving this charge balanced waveform, as explained indetail in the specification above: (1) the charging capacitor is chargedto a specific charge voltage, i.e., this specific charge voltage is nota system variable; (2) the current is controlled by the patientimpedance $\left( {I = \frac{V}{R}} \right),$

[0125] i.e., the current is not a system variable; and (3) the durationof the defibrillation pulse is controlled by the expected cellularresponse curve, i.e., duration is not a system variable. Because items1-3 are not system variables but rather are preset or set in accordanceto the patient at hand, the energy must be allowed to vary or thedefibrillation system is over constrained and charge balancing cannot beachieved over the range of patient impedances. To deliver fixed energyin a charge balanced system would require the ability to vary the chargevoltage. Varying the charge voltage is typically not done since thisrequires knowing the exact impedance in advance of the shock delivery.Many defibrillators measure the impedance during a high voltage chargedelivery since this is more accurate than low voltage measurements doneprior to shock delivery. Varying charge voltage also requires a moreexpensive defibrillation circuitry since capacitor costs increasedramatically with voltage.

[0126] It should be noted that due to the characteristics of thecellular response curve, the duration of the defibrillation pulse doesincrease slightly for increases in patient impedance. This increasedduration is of a much lesser effect than in a traditional truncatedwaveform.

[0127] As such, to exactly terminate the defibrillation waveform whenthe cellular response curve returns to zero charge (FIG. 8), the energyof the defibrillation waveform may be allowed to vary in the delivery ofthe first phase Ø₁ or, alternatively, in the delivery of the secondphase Ø₂.

[0128] With respect to the first phase Ø₁, the energy is allowed to varyper each patient 20 encounter by setting the time duration t₁ of Ø₁. Asnoted by the iterations of equation 42, the optimal ratio of duration ofØ₁ and Ø₂ occurs when t₁=t₂ or when τ₂=T_(M)=R_(H) C_(S) where R_(H) isthe measured variable heart resistance and C_(S) is the systemcapacitance including the capacitance of the first bank of capacitorsthat are operative with the delivery of the first phase. As τ_(M) isfixed and R_(H) is measured, the value of capacitance C_(S) is matchedto the resistance R_(H). Because the value of the capacitance is matchedto the resistance for the delivery of the first phase Ø₁, i.e., it isnot matched to a desired amount of fixed energy to be delivered, it canbe seen that the amount of energy is allowed to vary specific to and pereach patient encounter.

[0129] Likewise, with respect to the second phase Ø₂, the energy isallowed to vary per each patient encounter by setting the time durationof Ø₂. As noted by the iterations of equation 42, the optimal ratio ofduration of Ø₁ and Ø₂ occurs when t₁=t₂ or when τ₂=τ_(M)=R_(H) C_(S)where R_(H) is the measured variable heart resistance and C_(S) is thesystem capacitance including the capacitance of the second bank ofcapacitors that are operative with the delivery of the second phase Ø₂.As τ₂ is fixed and R_(H) is measured, the value of capacitance C_(S) ismatched to the resistance R_(H). Because the value of the capacitance ismatched to the resistance for the delivery of the second phase Ø₂, i.e.,it is not matched to a desired amount of fixed energy to be delivered,it can be seen that the amount of energy is allowed to vary specific toand per each patient encounter.

[0130] Although the present invention has been described with referenceto preferred embodiments, workers skilled in the art will recognize thatchanges may be made in form and detail without departing from the spiritor scope of the present invention.

What is claimed:
 1. A method for determining a first and a second phaseof a biphasic defibrillation shock pulse, one of said first phase andsaid second phase having variable energy, wherein upon application ofsaid first phase and said second phase of said biphasic defibrillationshock pulse a desired response is produced in a patient's cardiac cellmembrane, comprising: providing a quantitative model of a defibrillatorcircuit for producing said biphasic defibrillation shock pulse;providing a quantitative model of a patient that includes a variableheart component; providing a quantitative description of a predeterminedresponse of said cardiac cell membrane to said shock pulse; anddetermining a quantitative description of a first phase and a secondphase of said biphasic defibrillation shock pulse by selecting from agroup consisting of items (a) and (b) as defined below: (a) determininga quantitative description of a first phase of said biphasicdefibrillation shock pulse that will produce said predetermined responseof said cardiac cell membrane, wherein the determination is made as afunction of said predetermined response of said cardiac cell membrane,said quantitative model of a defibrillator circuit, and saidquantitative model of a patient, and wherein the quantitativedescription of the first phase provides for setting a time duration forsaid first phase based on said variable heart component, whereby anamount of energy to be delivered by said first phase varies according tothe time duration that is set; and determining a quantitativedescription of a second phase of said biphasic defibrillation shockpulse phase on said first phase; and (b) determining a quantitativedescription of a first phase of said biphasic defibrillation shock pulsethat will produce said predetermined response of said cardiac cellmembrane, wherein the determination is made as a function of saidpredetermined response of said cardiac cell membrane, said quantitativemodel of a defibrillator circuit, and said quantitative model of apatient; and determining a quantitative description of a second phase ofsaid biphasic defibrillation shock pulse based on said first phase,wherein said quantitative description provides for setting a timeduration for said second phase based on said variable heart componentwhereby an amount of energy to be delivered by said second phase variesaccording to said time duration that is set.